Royal Caribbean does these cruises, too. They're mostly 4 nights or 7 nights or longer. I did a Med cruise this past October but it was roundtrip out of Venice. I cruised with singles of all ages and I think it was mostly a youngish crowd, 40s or younger. It was on Splendour of the Seas which is about 12 years old and loved it. The food on the mass market lines isn't great anymore, unfortunately, but if you go with a more upscale line like Azamara or Holland America, you'll end up with a much older crowd. It's really all about the ports anyway so the ship is secondary, at least in my mind.

Carnival is or has already departed the European market. Costa might be another choice but I don't know much about them.

As I usually do with cruise questions, I recommend you check out cruisecritic.com for more information on everything cruise-related. I also like Cordelli's recommendation to order the DVDs, but remember the customers (i.e., women) depicted on the video may not always be similar to the customers on your cruise. It ain't called "advertising" for nothing!